Let D be the set of all calendar dates from 4/30/1789 to 9/2

Let D be the set of all calendar dates from 4/30/1789 to 9/25/2014.
Let P be the set of names of U.S. presidents.
Let F be the set of names of first ladies of the U.S.

Consider the following two functions press : D ⇒ P where  pres(d)  is the name of the president of the U.S. on date  d  (the incumbent on inauguration days, to avoid ambiguity) and   lady : P ⇒ F   where   lady(p)   is the name of the first lady of the U.S. during the presidency of president   P.

1. Can the composition  pres ° lady   be defined?  What about  lady °  pres ?2. Which of the following functional inverses exist and which do not?
   pres-1, lady-1, (lady°pres)-1, (pres°lady)-1   (the -1 should be in superscript)Thank you.